a = 0.1;
b = 0.3;
r = 1.0;

N = 200;

theta = linspace(0,2*pi,N);
theta_extrema = [1.673, 3.447, 4.610, 5.978];
x = a + r*cos(theta);
y = b + r*sin(theta);
z = x.*y;
x_extrema = a + r*cos(theta_extrema);
y_extrema = b + r*sin(theta_extrema);
z_extrema = x_extrema.*y_extrema;

l1norm = abs(x) + abs(y) + abs(z);

figure; % Create a new figure
plot3(0, 0, 0, 'o', 'MarkerFaceColor', 'r'); % Scatter-like plot
hold on
plot3(1, 2, 1, 'o', 'MarkerFaceColor', 'r'); % Scatter-like plot
plot3(x, y, z, 'x', 'MarkerFaceColor', 'b'); % Scatter-like plot
plot3(x_extrema, y_extrema, z_extrema, 'o', 'MarkerFaceColor', 'k'); % Scatter-like plot

grid on; % Enable grid for better visualization
xlabel('X');
ylabel('Y');
zlabel('Z');
axis equal
title('3D Scatter Plot');